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ERC FUNDED PROJECTS

Project1D-electrons coupled to dissipation: a novel approach for understanding and engineering superconducting materials and devices

Researcher (PI)Adrian KANTIAN

Host Institution (HI)UPPSALA UNIVERSITET

Call DetailsStarting Grant (StG), PE3, ERC-2017-STG

SummaryCorrelated electrons are at the forefront of condensed matter theory. Interacting quasi-1D electrons have seen vast progress in analytical and numerical theory, and thus in fundamental understanding and quantitative prediction. Yet, in the 1D limit fluctuations preclude important technological use, particularly of superconductors. In contrast, high-Tc superconductors in 2D/3D are not precluded by fluctuations, but lack a fundamental theory, making prediction and engineering of their properties, a major goal in physics, very difficult. This project aims to combine the advantages of both areas by making major progress in the theory of quasi-1D electrons coupled to an electron bath, in part building on recent breakthroughs (with the PIs extensive involvement) in simulating 1D and 2D electrons with parallelized density matrix renormalization group (pDMRG) numerics. Such theory will fundamentally advance the study of open electron systems, and show how to use 1D materials as elements of new superconducting (SC) devices and materials: 1) It will enable a new state of matter, 1D electrons with true SC order. Fluctuations from the electronic liquid, such as graphene, could also enable nanoscale wires to appear SC at high temperatures. 2) A new approach for the deliberate engineering of a high-Tc superconductor. In 1D, how electrons pair by repulsive interactions is understood and can be predicted. Stabilization by reservoir - formed by a parallel array of many such 1D systems - offers a superconductor for which all factors setting Tc are known and can be optimized. 3) Many existing superconductors with repulsive electron pairing, all presently not understood, can be cast as 1D electrons coupled to a bath. Developing chain-DMFT theory based on pDMRG will allow these materials SC properties to be simulated and understood for the first time. 4) The insights gained will be translated to 2D superconductors to study how they could be enhanced by contact with electronic liquids.

Correlated electrons are at the forefront of condensed matter theory. Interacting quasi-1D electrons have seen vast progress in analytical and numerical theory, and thus in fundamental understanding and quantitative prediction. Yet, in the 1D limit fluctuations preclude important technological use, particularly of superconductors. In contrast, high-Tc superconductors in 2D/3D are not precluded by fluctuations, but lack a fundamental theory, making prediction and engineering of their properties, a major goal in physics, very difficult. This project aims to combine the advantages of both areas by making major progress in the theory of quasi-1D electrons coupled to an electron bath, in part building on recent breakthroughs (with the PIs extensive involvement) in simulating 1D and 2D electrons with parallelized density matrix renormalization group (pDMRG) numerics. Such theory will fundamentally advance the study of open electron systems, and show how to use 1D materials as elements of new superconducting (SC) devices and materials: 1) It will enable a new state of matter, 1D electrons with true SC order. Fluctuations from the electronic liquid, such as graphene, could also enable nanoscale wires to appear SC at high temperatures. 2) A new approach for the deliberate engineering of a high-Tc superconductor. In 1D, how electrons pair by repulsive interactions is understood and can be predicted. Stabilization by reservoir - formed by a parallel array of many such 1D systems - offers a superconductor for which all factors setting Tc are known and can be optimized. 3) Many existing superconductors with repulsive electron pairing, all presently not understood, can be cast as 1D electrons coupled to a bath. Developing chain-DMFT theory based on pDMRG will allow these materials SC properties to be simulated and understood for the first time. 4) The insights gained will be translated to 2D superconductors to study how they could be enhanced by contact with electronic liquids.

Max ERC Funding

1 491 013 €

Duration

Start date: 2018-10-01, End date: 2023-09-30

Project acronym3DWATERWAVES

ProjectMathematical aspects of three-dimensional water waves with vorticity

Researcher (PI)Erik Torsten Wahlén

Host Institution (HI)LUNDS UNIVERSITET

Call DetailsStarting Grant (StG), PE1, ERC-2015-STG

SummaryThe goal of this project is to develop a mathematical theory for steady three-dimensional water waves with vorticity. The mathematical model consists of the incompressible Euler equations with a free surface, and vorticity is important for modelling the interaction of surface waves with non-uniform currents. In the two-dimensional case, there has been a lot of progress on water waves with vorticity in the last decade. This progress has mainly been based on the stream function formulation, in which the problem is reformulated as a nonlinear elliptic free boundary problem. An analogue of this formulation is not available in three dimensions, and the theory has therefore so far been restricted to irrotational flow. In this project we seek to go beyond this restriction using two different approaches. In the first approach we will adapt methods which have been used to construct three-dimensional ideal flows with vorticity in domains with a fixed boundary to the free boundary context (for example Beltrami flows). In the second approach we will develop methods which are new even in the case of a fixed boundary, by performing a detailed study of the structure of the equations close to a given shear flow using ideas from infinite-dimensional bifurcation theory. This involves handling infinitely many resonances.

The goal of this project is to develop a mathematical theory for steady three-dimensional water waves with vorticity. The mathematical model consists of the incompressible Euler equations with a free surface, and vorticity is important for modelling the interaction of surface waves with non-uniform currents. In the two-dimensional case, there has been a lot of progress on water waves with vorticity in the last decade. This progress has mainly been based on the stream function formulation, in which the problem is reformulated as a nonlinear elliptic free boundary problem. An analogue of this formulation is not available in three dimensions, and the theory has therefore so far been restricted to irrotational flow. In this project we seek to go beyond this restriction using two different approaches. In the first approach we will adapt methods which have been used to construct three-dimensional ideal flows with vorticity in domains with a fixed boundary to the free boundary context (for example Beltrami flows). In the second approach we will develop methods which are new even in the case of a fixed boundary, by performing a detailed study of the structure of the equations close to a given shear flow using ideas from infinite-dimensional bifurcation theory. This involves handling infinitely many resonances.

Summary"High-energy observations of our Galaxy offer a good, albeit not complete, picture of the X-ray source populations, in particular the accreting binary sources. Recent ability to study accreting binaries in nearby galaxies has shown that we would be short-sighted if we restricted ourselves to our Galaxy or to a few nearby ones. I propose an ambitious project that involves a comprehensive study of all the galaxies within 10 Mpc for which we can study in detail their X-ray sources and stellar populations. The study will combine data from a unique suite of observatories (Chandra, XMM-Newton, HST, Spitzer) with state-of-the-art theoretical modelling of binary systems. I propose a novel approach that links the accreting binary populations to their parent stellar populations and surpasses any current studies of X-ray binary populations, both in scale and in scope, by: (a) combining methods and results from several different areas of astrophysics (compact objects, binary systems, stellar populations, galaxy evolution); (b) using data from almost the whole electromagnetic spectrum (infrared to X-ray bands); (c) identifying and studying the different sub-populations of accreting binaries; and (d) performing direct comparison between observations and theoretical predictions, over a broad parameter space. The project: (a) will answer the long-standing question of the formation efficiency of accreting binaries in different environments; and (b) will constrain their evolutionary paths. As by-products the project will provide eagerly awaited input to the fields of gravitational-wave sources, γ-ray bursts, and X-ray emitting galaxies at cosmological distances and it will produce a heritage multi-wavelength dataset and library of models for future studies of galaxies and accreting binaries."

"High-energy observations of our Galaxy offer a good, albeit not complete, picture of the X-ray source populations, in particular the accreting binary sources. Recent ability to study accreting binaries in nearby galaxies has shown that we would be short-sighted if we restricted ourselves to our Galaxy or to a few nearby ones. I propose an ambitious project that involves a comprehensive study of all the galaxies within 10 Mpc for which we can study in detail their X-ray sources and stellar populations. The study will combine data from a unique suite of observatories (Chandra, XMM-Newton, HST, Spitzer) with state-of-the-art theoretical modelling of binary systems. I propose a novel approach that links the accreting binary populations to their parent stellar populations and surpasses any current studies of X-ray binary populations, both in scale and in scope, by: (a) combining methods and results from several different areas of astrophysics (compact objects, binary systems, stellar populations, galaxy evolution); (b) using data from almost the whole electromagnetic spectrum (infrared to X-ray bands); (c) identifying and studying the different sub-populations of accreting binaries; and (d) performing direct comparison between observations and theoretical predictions, over a broad parameter space. The project: (a) will answer the long-standing question of the formation efficiency of accreting binaries in different environments; and (b) will constrain their evolutionary paths. As by-products the project will provide eagerly awaited input to the fields of gravitational-wave sources, γ-ray bursts, and X-ray emitting galaxies at cosmological distances and it will produce a heritage multi-wavelength dataset and library of models for future studies of galaxies and accreting binaries."

Max ERC Funding

1 242 000 €

Duration

Start date: 2014-04-01, End date: 2019-03-31

Project acronymADAPTIVES

ProjectAlgorithmic Development and Analysis of Pioneer Techniques for Imaging with waVES

Researcher (PI)Chrysoula Tsogka

Host Institution (HI)FOUNDATION FOR RESEARCH AND TECHNOLOGY HELLAS

Call DetailsStarting Grant (StG), PE1, ERC-2009-StG

SummaryThe proposed work concerns the theoretical and numerical development of robust and adaptive methodologies for broadband imaging in clutter. The word clutter expresses our uncertainty on the wave speed of the propagation medium. Our results are expected to have a strong impact in a wide range of applications, including underwater acoustics, exploration geophysics and ultrasound non-destructive testing. Our machinery is coherent interferometry (CINT), a state-of-the-art statistically stable imaging methodology, highly suitable for the development of imaging methods in clutter. We aim to extend CINT along two complementary directions: novel types of applications, and further mathematical and numerical development so as to assess and extend its range of applicability. CINT is designed for imaging with partially coherent array data recorded in richly scattering media. It uses statistical smoothing techniques to obtain results that are independent of the clutter realization. Quantifying the amount of smoothing needed is difficult, especially when there is no a priori knowledge about the propagation medium. We intend to address this question by coupling the imaging process with the estimation of the medium's large scale features. Our algorithms rely on the residual coherence in the data. When the coherent signal is too weak, the CINT results are unsatisfactory. We propose two ways for enhancing the resolution of CINT: filter the data prior to imaging (noise reduction) and waveform design (optimize the source distribution). Finally, we propose to extend the applicability of our imaging-in-clutter methodologies by investigating the possibility of utilizing ambient noise sources to perform passive sensor imaging, as well as by studying the imaging problem in random waveguides.

The proposed work concerns the theoretical and numerical development of robust and adaptive methodologies for broadband imaging in clutter. The word clutter expresses our uncertainty on the wave speed of the propagation medium. Our results are expected to have a strong impact in a wide range of applications, including underwater acoustics, exploration geophysics and ultrasound non-destructive testing. Our machinery is coherent interferometry (CINT), a state-of-the-art statistically stable imaging methodology, highly suitable for the development of imaging methods in clutter. We aim to extend CINT along two complementary directions: novel types of applications, and further mathematical and numerical development so as to assess and extend its range of applicability. CINT is designed for imaging with partially coherent array data recorded in richly scattering media. It uses statistical smoothing techniques to obtain results that are independent of the clutter realization. Quantifying the amount of smoothing needed is difficult, especially when there is no a priori knowledge about the propagation medium. We intend to address this question by coupling the imaging process with the estimation of the medium's large scale features. Our algorithms rely on the residual coherence in the data. When the coherent signal is too weak, the CINT results are unsatisfactory. We propose two ways for enhancing the resolution of CINT: filter the data prior to imaging (noise reduction) and waveform design (optimize the source distribution). Finally, we propose to extend the applicability of our imaging-in-clutter methodologies by investigating the possibility of utilizing ambient noise sources to perform passive sensor imaging, as well as by studying the imaging problem in random waveguides.

Max ERC Funding

690 000 €

Duration

Start date: 2010-06-01, End date: 2015-11-30

Project acronymAFRODITE

ProjectAdvanced Fluid Research On Drag reduction In Turbulence Experiments

Researcher (PI)Jens Henrik Mikael Fransson

Host Institution (HI)KUNGLIGA TEKNISKA HOEGSKOLAN

Call DetailsStarting Grant (StG), PE8, ERC-2010-StG_20091028

SummaryA hot topic in today's debate on global warming is drag reduction in aeronautics. The most beneficial concept for drag reduction is to maintain the major portion of the airfoil laminar. Estimations show that the potential drag reduction can be as much as 15%, which would give a significant reduction of NOx and CO emissions in the atmosphere considering that the number of aircraft take offs, only in the EU, is over 19 million per year. An important element for successful flow control, which can lead to a reduced aerodynamic drag, is enhanced physical understanding of the transition to turbulence process.
In previous wind tunnel measurements we have shown that roughness elements can be used to sensibly delay transition to turbulence. The result is revolutionary, since the common belief has been that surface roughness causes earlier transition and in turn increases the drag, and is a proof of concept of the passive control method per se. The beauty with a passive control technique is that no external energy has to be added to the flow system in order to perform the control, instead one uses the existing energy in the flow.
In this project proposal, AFRODITE, we will take this passive control method to the next level by making it twofold, more persistent and more robust. Transition prevention is the goal rather than transition delay and the method will be extended to simultaneously control separation, which is another unwanted flow phenomenon especially during airplane take offs. AFRODITE will be a catalyst for innovative research, which will lead to a cleaner sky.

A hot topic in today's debate on global warming is drag reduction in aeronautics. The most beneficial concept for drag reduction is to maintain the major portion of the airfoil laminar. Estimations show that the potential drag reduction can be as much as 15%, which would give a significant reduction of NOx and CO emissions in the atmosphere considering that the number of aircraft take offs, only in the EU, is over 19 million per year. An important element for successful flow control, which can lead to a reduced aerodynamic drag, is enhanced physical understanding of the transition to turbulence process.
In previous wind tunnel measurements we have shown that roughness elements can be used to sensibly delay transition to turbulence. The result is revolutionary, since the common belief has been that surface roughness causes earlier transition and in turn increases the drag, and is a proof of concept of the passive control method per se. The beauty with a passive control technique is that no external energy has to be added to the flow system in order to perform the control, instead one uses the existing energy in the flow.
In this project proposal, AFRODITE, we will take this passive control method to the next level by making it twofold, more persistent and more robust. Transition prevention is the goal rather than transition delay and the method will be extended to simultaneously control separation, which is another unwanted flow phenomenon especially during airplane take offs. AFRODITE will be a catalyst for innovative research, which will lead to a cleaner sky.

Max ERC Funding

1 418 399 €

Duration

Start date: 2010-11-01, End date: 2015-10-31

Project acronymALMA

ProjectAttosecond Control of Light and Matter

Researcher (PI)Anne L'huillier

Host Institution (HI)LUNDS UNIVERSITET

Call DetailsAdvanced Grant (AdG), PE2, ERC-2008-AdG

SummaryAttosecond light pulses are generated when an intense laser interacts with a gas target. These pulses are not only short, enabling the study of electronic processes at their natural time scale, but also coherent. The vision of this proposal is to extend temporal coherent control concepts to a completely new regime of time and energy, combining (i) ultrashort pulses (ii) broadband excitation (iii) high photon energy, allowing scientists to reach not only valence but also inner shells in atoms and molecules, and, when needed, (iv) high spatial resolution. We want to explore how elementary electronic processes in atoms, molecules and more complex systems can be controlled by using well designed sequences of attosecond pulses. The research project proposed is organized into four parts: 1. Attosecond control of light leading to controlled sequences of attosecond pulses We will develop techniques to generate sequences of attosecond pulses with a variable number of pulses and controlled carrier-envelope-phase variation between consecutive pulses. 2. Attosecond control of electronic processes in atoms and molecules We will investigate the dynamics and coherence of phenomena induced by attosecond excitation of electron wave packets in various systems and we will explore how they can be controlled by a controlled sequence of ultrashort pulses. 3. Intense attosecond sources to reach the nonlinear regime We will optimize attosecond light sources in a systematic way, including amplification of the radiation by injecting a free electron laser. This will open up the possibility to develop nonlinear measurement and control schemes. 4. Attosecond control in more complex systems, including high spatial resolution We will develop ultrafast microscopy techniques, in order to obtain meaningful temporal information in surface and solid state physics. Two directions will be explored, digital in line microscopic holography and photoemission electron microscopy.

Attosecond light pulses are generated when an intense laser interacts with a gas target. These pulses are not only short, enabling the study of electronic processes at their natural time scale, but also coherent. The vision of this proposal is to extend temporal coherent control concepts to a completely new regime of time and energy, combining (i) ultrashort pulses (ii) broadband excitation (iii) high photon energy, allowing scientists to reach not only valence but also inner shells in atoms and molecules, and, when needed, (iv) high spatial resolution. We want to explore how elementary electronic processes in atoms, molecules and more complex systems can be controlled by using well designed sequences of attosecond pulses. The research project proposed is organized into four parts: 1. Attosecond control of light leading to controlled sequences of attosecond pulses We will develop techniques to generate sequences of attosecond pulses with a variable number of pulses and controlled carrier-envelope-phase variation between consecutive pulses. 2. Attosecond control of electronic processes in atoms and molecules We will investigate the dynamics and coherence of phenomena induced by attosecond excitation of electron wave packets in various systems and we will explore how they can be controlled by a controlled sequence of ultrashort pulses. 3. Intense attosecond sources to reach the nonlinear regime We will optimize attosecond light sources in a systematic way, including amplification of the radiation by injecting a free electron laser. This will open up the possibility to develop nonlinear measurement and control schemes. 4. Attosecond control in more complex systems, including high spatial resolution We will develop ultrafast microscopy techniques, in order to obtain meaningful temporal information in surface and solid state physics. Two directions will be explored, digital in line microscopic holography and photoemission electron microscopy.

Max ERC Funding

2 250 000 €

Duration

Start date: 2008-12-01, End date: 2013-11-30

Project acronymALPAM

ProjectAtomic-Level Physics of Advanced Materials

Researcher (PI)Börje Johansson

Host Institution (HI)KUNGLIGA TEKNISKA HOEGSKOLAN

Call DetailsAdvanced Grant (AdG), PE5, ERC-2008-AdG

SummaryMost of the technological materials have been developed by very expensive and cumbersome trial and error methods. On the other hand, computer based theoretical design of advanced materials is an area where rapid and extensive developments are taking place. Within my group new theoretical tools have now been established which are extremely well suited to the study of complex materials. In this approach basic quantum mechanical theories are used to describe fundamental properties of alloys and compounds. The utilization of such calculations to investigate possible optimizations of certain key properties represents a major departure from the traditional design philosophy. The purpose of my project is to build up a new competence in the field of computer-aided simulations of advanced materials. The main goal will be to achieve a deep understanding of the behaviour of complex metallic systems under equilibrium and non-equilibrium conditions at the atomic level by studying their electronic, magnetic and atomic structure using the most modern and advanced computational methods. This will enable us to establish a set of materials parameters and composition-structure-property relations that are needed for materials optimization.
The research will be focused on fundamental technological properties related to defects in advanced metallic alloys (high-performance steels, superalloys, and refractory, energy related and geochemical materials) and alloy phases (solid solutions, intermetallic compounds), which will be studied by means of parameter free atomistic simulations combined with continuum modelling. As a first example, we will study the Fe-Cr system, which is of great interest to industry as well as in connection to nuclear waste. The Fe-Cr-Ni system will form another large group of materials under the aegis of this project. Special emphasis will also be placed on those Fe-alloys which exist under extreme conditions and are possible candidates for the Earth core.

Most of the technological materials have been developed by very expensive and cumbersome trial and error methods. On the other hand, computer based theoretical design of advanced materials is an area where rapid and extensive developments are taking place. Within my group new theoretical tools have now been established which are extremely well suited to the study of complex materials. In this approach basic quantum mechanical theories are used to describe fundamental properties of alloys and compounds. The utilization of such calculations to investigate possible optimizations of certain key properties represents a major departure from the traditional design philosophy. The purpose of my project is to build up a new competence in the field of computer-aided simulations of advanced materials. The main goal will be to achieve a deep understanding of the behaviour of complex metallic systems under equilibrium and non-equilibrium conditions at the atomic level by studying their electronic, magnetic and atomic structure using the most modern and advanced computational methods. This will enable us to establish a set of materials parameters and composition-structure-property relations that are needed for materials optimization.
The research will be focused on fundamental technological properties related to defects in advanced metallic alloys (high-performance steels, superalloys, and refractory, energy related and geochemical materials) and alloy phases (solid solutions, intermetallic compounds), which will be studied by means of parameter free atomistic simulations combined with continuum modelling. As a first example, we will study the Fe-Cr system, which is of great interest to industry as well as in connection to nuclear waste. The Fe-Cr-Ni system will form another large group of materials under the aegis of this project. Special emphasis will also be placed on those Fe-alloys which exist under extreme conditions and are possible candidates for the Earth core.

SummaryThis proposal targets the emerging frontier research field of multiple-input multiple-output (MIMO) systems along with several innovative and somewhat unconventional applications of such systems. The use of arrays of transmitters and receivers will have a profound impact on future medical imaging/therapy systems, radar systems, and radio communication networks. Multiple transmitters provide a tremendous versatility and allow waveforms to be adapted temporally and spatially to environmental conditions. This is useful for individually tailored illumination of human tissue in biomedical imaging or ultrasound therapy. In radar systems, multiple transmit beams can be formed simultaneously via separate waveform designs allowing accurate target classification. In a wireless communication system, multiple communication signals can be directed to one or more users at the same time on the same frequency carrier. In addition, multiple receivers can be used in the above applications to provide increased detection performance, interference rejection, and improved estimation accuracy. The joint modelling, analysis, and design of these multidimensional transmit and receive schemes form the core of this research proposal. Ultimately, our research aims at developing the fundamental tools that will allow the design of wireless communication systems with an order-of-magnitude higher capacity at a lower cost than today; of ultrasound therapy systems maximizing delivered power while reducing treatment duration and unwanted illumination; and of distributed aperture multi-beam radars allowing more effective target location, identification, and classification. Europe has several successful industries that are active in biomedical imaging/therapy, radar systems, and wireless communications. The future success of these sectors critically depends on the ability to innovate and integrate new technology.

This proposal targets the emerging frontier research field of multiple-input multiple-output (MIMO) systems along with several innovative and somewhat unconventional applications of such systems. The use of arrays of transmitters and receivers will have a profound impact on future medical imaging/therapy systems, radar systems, and radio communication networks. Multiple transmitters provide a tremendous versatility and allow waveforms to be adapted temporally and spatially to environmental conditions. This is useful for individually tailored illumination of human tissue in biomedical imaging or ultrasound therapy. In radar systems, multiple transmit beams can be formed simultaneously via separate waveform designs allowing accurate target classification. In a wireless communication system, multiple communication signals can be directed to one or more users at the same time on the same frequency carrier. In addition, multiple receivers can be used in the above applications to provide increased detection performance, interference rejection, and improved estimation accuracy. The joint modelling, analysis, and design of these multidimensional transmit and receive schemes form the core of this research proposal. Ultimately, our research aims at developing the fundamental tools that will allow the design of wireless communication systems with an order-of-magnitude higher capacity at a lower cost than today; of ultrasound therapy systems maximizing delivered power while reducing treatment duration and unwanted illumination; and of distributed aperture multi-beam radars allowing more effective target location, identification, and classification. Europe has several successful industries that are active in biomedical imaging/therapy, radar systems, and wireless communications. The future success of these sectors critically depends on the ability to innovate and integrate new technology.

Max ERC Funding

1 872 720 €

Duration

Start date: 2009-01-01, End date: 2013-12-31

Project acronymANSR

ProjectAb initio approach to nuclear structure and reactions (++)

Researcher (PI)Christian Erik Forssén

Host Institution (HI)CHALMERS TEKNISKA HOEGSKOLA AB

Call DetailsStarting Grant (StG), PE2, ERC-2009-StG

SummaryToday, much interest in several fields of physics is devoted to the study of small, open quantum systems, whose properties are profoundly affected by the environment; i.e., the continuum of decay channels. In nuclear physics, these problems were originally studied in the context of nuclear reactions but their importance has been reestablished with the advent of radioactive-beam physics and the resulting interest in exotic nuclei. In particular, strong theory initiatives in this area of research will be instrumental for the success of the experimental program at the Facility for Antiproton and Ion Research (FAIR) in Germany. In addition, many of the aspects of open quantum systems are also being explored in the rapidly evolving research on ultracold atomic gases, quantum dots, and other nanodevices. A first-principles description of open quantum systems presents a substantial theoretical and computational challenge. However, the current availability of enormous computing power has allowed theorists to make spectacular progress on problems that were previously thought intractable. The importance of computational methods to study quantum many-body systems is stressed in this proposal. Our approach is based on the ab initio no-core shell model (NCSM), which is a well-established theoretical framework aimed originally at an exact description of nuclear structure starting from realistic inter-nucleon forces. A successful completion of this project requires extensions of the NCSM mathematical framework and the development of highly advanced computer codes. The &apos;++&apos; in the project title indicates the interdisciplinary aspects of the present research proposal and the ambition to make a significant impact on connected fields of many-body physics.

Today, much interest in several fields of physics is devoted to the study of small, open quantum systems, whose properties are profoundly affected by the environment; i.e., the continuum of decay channels. In nuclear physics, these problems were originally studied in the context of nuclear reactions but their importance has been reestablished with the advent of radioactive-beam physics and the resulting interest in exotic nuclei. In particular, strong theory initiatives in this area of research will be instrumental for the success of the experimental program at the Facility for Antiproton and Ion Research (FAIR) in Germany. In addition, many of the aspects of open quantum systems are also being explored in the rapidly evolving research on ultracold atomic gases, quantum dots, and other nanodevices. A first-principles description of open quantum systems presents a substantial theoretical and computational challenge. However, the current availability of enormous computing power has allowed theorists to make spectacular progress on problems that were previously thought intractable. The importance of computational methods to study quantum many-body systems is stressed in this proposal. Our approach is based on the ab initio no-core shell model (NCSM), which is a well-established theoretical framework aimed originally at an exact description of nuclear structure starting from realistic inter-nucleon forces. A successful completion of this project requires extensions of the NCSM mathematical framework and the development of highly advanced computer codes. The &apos;++&apos; in the project title indicates the interdisciplinary aspects of the present research proposal and the ambition to make a significant impact on connected fields of many-body physics.

Max ERC Funding

1 304 800 €

Duration

Start date: 2009-12-01, End date: 2014-11-30

Project acronymAPPROXNP

ProjectApproximation of NP-hard optimization problems

Researcher (PI)Johan Håstad

Host Institution (HI)KUNGLIGA TEKNISKA HOEGSKOLAN

Call DetailsAdvanced Grant (AdG), PE6, ERC-2008-AdG

SummaryThe proposed project aims to create a center of excellence that aims at understanding the approximability of NP-hard optimization problems. In particular, for central problems like vertex cover, coloring of graphs, and various constraint satisfaction problems we want to study upper and lower bounds on how well they can be approximated in polynomial time. Many existing strong results are based on what is known as the Unique Games Conjecture (UGC) and a significant part of the project will be devoted to studying this conjecture. We expect that a major step needed to be taken in this process is to further develop the understanding of Boolean functions on the Boolean hypercube. We anticipate that the tools needed for this will come in the form of harmonic analysis which in its turn will rely on the corresponding results in the analysis of functions over the domain of real numbers.

The proposed project aims to create a center of excellence that aims at understanding the approximability of NP-hard optimization problems. In particular, for central problems like vertex cover, coloring of graphs, and various constraint satisfaction problems we want to study upper and lower bounds on how well they can be approximated in polynomial time. Many existing strong results are based on what is known as the Unique Games Conjecture (UGC) and a significant part of the project will be devoted to studying this conjecture. We expect that a major step needed to be taken in this process is to further develop the understanding of Boolean functions on the Boolean hypercube. We anticipate that the tools needed for this will come in the form of harmonic analysis which in its turn will rely on the corresponding results in the analysis of functions over the domain of real numbers.